TY - JOUR

T1 - Sampling, interpolation and Riesz bases in small Fock spaces

AU - Baranov, A.

AU - Dumont, A.

AU - Hartmann, A.

AU - Kellay, K.

PY - 2015

Y1 - 2015

N2 - © 2014 Elsevier Masson SAS.We give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets-Ingham 1/4 theorem for Paley-Wiener spaces. Contrary to the situation in Paley-Wiener spaces, a link can be established between Riesz bases in the Hilbert case and corresponding complete interpolating sequences in small Fock spaces with associated uniform norm. These results allow to show that if a sequence has a density strictly different from the critical one then either it can be completed or reduced to a complete interpolating sequence. In particular, this allows to give necessary and sufficient conditions for interpolation or sampling in terms of densities.

AB - © 2014 Elsevier Masson SAS.We give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets-Ingham 1/4 theorem for Paley-Wiener spaces. Contrary to the situation in Paley-Wiener spaces, a link can be established between Riesz bases in the Hilbert case and corresponding complete interpolating sequences in small Fock spaces with associated uniform norm. These results allow to show that if a sequence has a density strictly different from the critical one then either it can be completed or reduced to a complete interpolating sequence. In particular, this allows to give necessary and sufficient conditions for interpolation or sampling in terms of densities.

U2 - 10.1016/j.matpur.2014.11.002

DO - 10.1016/j.matpur.2014.11.002

M3 - Article

SP - 1358

EP - 1389

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

SN - 0021-7824

IS - 6

ER -